Following are the interactive versions of the circuits used in the document:

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Logic gates are used in a digital circuit to perform various operations and control flow in the circuit. There are various logic gates from basic to complex. Basic logic gates include, AND, OR, NOT, NAND, NOR, XOR, XNOR. Basic logic gates can be used to create other logic gates, like combining AND and NOT gives, NAND.

Basic Logic Gates

Following are the basic logic gates:

• NOT
• AND
• OR
• NAND
• NOR
• XOR
• XNOT

NOT gate

Truth table for NOT gate:

$A$	$X=\bar{A}$
0	1
1	0

AND gate

Truth table for AND gate:

$A$	$B$	$X=A.B$
0	0	0
0	1	0
1	0	0
1	1	1

OR gate

Truth table for OR gate:

$A$	$B$	$X=A.B$
0	0	0
0	1	1
1	0	1
1	1	1

NAND gate

Truth table for NAND gate:

$A$	$B$	$X=A.B$
0	0	1
0	1	1
1	0	1
1	1	0

NOR gate

Truth table for NOR gate:

$A$	$B$	$X=A.B$
0	0	1
0	1	0
1	0	0
1	1	0

XOR gate

Truth table for XOR gate:

$A$	$B$	$X=A.B$
0	0	0
0	1	1
1	0	1
1	1	0

XAND gate

Truth table for XAND gate:

$A$	$B$	$X=A.B$
0	0	1
0	1	0
1	0	0
1	1	1

Example 1: Draw logic circuit for $\bar{A}B(A+\bar{B}C)+A\bar{C}$.

Method 1: Using direct lines, the circuit can be drawm as:

Method 2: Using parallel lines, the circuit can be drawn as:

Example 2: Draw logic circuit for $\overline{\bar{A}C}(A+\bar{B}(A+\bar{B}\bar{C}))$

Following is the logic circuit for the above operation:

Universal Gates

NAND and NOR gates are called universal gates because they can be used to form any other gates.

Using NAND gate

NOT gate

AND gate

OR gate

Using NOR gate

NOT gate

AND gate

OR gate

Circuit Conversion

Using NAND only

NAND gate being an universal gate, can be used to convert all gates in a circuit to it, i.e., all gates within the circuit can be converted into NAND gate. The circuit thus will be made of only NAND gate. The steps to do so are:

1. For AND gates, the NOT will be placed infront of the gate towards the output.
2. For OR gates, the NOTs will be placed behind the gate from the inputs.
3. All NOTs infront of AND gate will be cancelled. Consequetively any NOT behind OR gate will be cancelled.
4. The circuit must be balanced. Any NOT added to the circuit must be countered with another NOT in the same line.

Example 3: Construct, $\bar{A}B(A+\bar{B}C)+A\bar{C}$ using NAND gates only.

Circuit using normal gates:

In the above circuit, NOT gates from the main line will be converted into, NAND-NOT circuit. The AND gate operating $\bar{B}C$, will have a NOT infront of it, which will be countered by the NOT behind the frontal OR gate. The frontal OR's second input coming from $A$ will be changed to $\bar{A}$ in order to counter for the NOT behind the OR gate. The AND gate operating $\bar{A}B$, will have a NOT infront of it, and since it is connected further to an AND gate, a NOT gate will be added to balance the circuit. The final OR will receive two NOTs from the preceeding ANDs, and give the final result.

Final circuit using NAND gates only:

Exercise 1

1. Draw a circuit for $\overline{\bar{A}C}(A+\bar{B}(A+\bar{B}\bar{C}))$, using NAND gates only.

2. Draw a circuit for the following using NAND gates only:

   1. $\bar{A}(\bar{B}C+\bar{A}(B+\bar{C})+A\bar{C})+\bar{B}C$
   2. $(A\bar{C}+\bar{A}(B+\bar{A}))(\bar{B}(A+\bar{B})+\bar{A}\bar{C})$
   3. $\bar{A}(\bar{C}(\bar{A}B+\bar{C})+\bar{B}(\bar{A}\bar{C}+B))$